NTA Abhyas JEE Main2020MathematicsStatisticsPractice

The mean of n items is x - . If the first item is increased by n , second by n - 1 and so on and last by 1, then the new mean is

Options

Ax - + n n + 1 2 n + 1 6
Bx - + n + 1 2 n + 1 6
Cx - + n + 1 2
Dx - + n + 1 4

Correct answer

C. x - + n + 1 2

Step-by-step solution

Let, x 1 , x 2 , … … . . x n be n items. Then, x - = 1 n ∑ x i . Let, y 1 = x 1 + n , y 2 = x 2 + n - 1 y 3 = x 3 + n - 2 , … … . , y n = x n + 1 Then, the mean of the new series is 1 n ∑ y i = 1 n ∑ x i + 1 n n + n - 1 + n - 2 + . … … . 1 = x ¯ + 1 n ⋅ n n + 1 2 = x ¯ + n + 1 2

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